Holographic principle

I've finished reading Brian Greene's "Fabric of the Cosmos" and the last chapter intrigued me.

He talks about how Hawking et al have proven that the maximum entropy inside a black hole is a function of the surface area of the BH, not the volume. This can be expanded to any volume of space, ultimately leading to the conclusion that the maximum entropy of (and thus the maximum information containable within) any volume of space is a function of its surface area.

(Wait for it, there's a question at the end of all this)

This places a constraint on the freedoms with which anything within that volume can be described, which implies a limit on our free will. (I am greatly simplifying.)

Generalizing: no matter how many dimensions a volume has, it can be described using n-1 dimensions (eg. a 4 dimensional space has a 3 dimensional surface area and can only contain as much information as can be described upon its surface).

So, my question:

If our universe turns out to have 10 or 11 dimensions, it would only take the loss of one of them (or equivalent loss, divided up among more than one) to satisfy this constraint. This would leave complete freedom in all dimensions that are experienced by us.

Holography and the Bekenstein Bound STRONGLY suggests that spacetime is emergent from computational processes in 2 DIMENSIONS and that the fundamental particle is a bit of information- thus any theory positing 10-11 dimensions must be a result of the degrees of freedom of the computation- not a physically higher dimensional background metric- the computational/information based perspective which yields the holographic principle implies that dimensionality at fundamental levels is LESS than observed [built up from the computational graph] as opposed to the notion of fundamentaly higher dimensions